# Please give an example in $\mathbb{R}^{n}$ of a set that satisfies the upper bound in the Kuratowski Closure-Complement Theorem.

Please give an example in $\mathbb{R}^{n}$ of a set $T$ that satisfies the upper bound of $14$ in the Kuratowski Closure-Complement Theorem. Thanks!

The standard example in $\mathbb{R}$ is $$(0,1) \cup (1,2) \cup \{ 3 \} \cup [(4,5) \cap \mathbb{Q}].$$
• However, the OP is asking for an example in $\mathbb{R}^{n}$. Is it trivial to construct such one from that in $\mathbb{R}$? – hengxin Jan 22 '14 at 5:11